Write an absolute value inequality whose solution set is shown by the graphs. Each mark on the graph represents a whole number. (Your answers will have the absolute value symbols, | |.)
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To answer this question we will use the following:
[tex]\begin{gathered} |a|\ge b\text{ if and only if} \\ a\ge b\text{ or }a\le-b. \end{gathered}[/tex]Notice that the given set consists of the real numbers that are greater than or equal to 3 or that are less than or equal to -3, the above statement in algebraic notation is:
[tex]x\geq3\text{ or }x\leq-3.[/tex]Using the first equations we get that the given set can be represented by the following absolute value inequality:
[tex]|x|\ge3.[/tex]Answer:
[tex]|x|\ge3.[/tex]Related Questions
Two sides of a ∆ have lengths 28cm and 82 cm. The measure of the third side is a whole number of centimeters. • What is the longest the third side can be? • What is the shortest the third side can be?
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You need to remember the Triangl inequality Theorem. This states that
Let be "a", "b" and "c" the sides of a triangle. According to the Theorem mentioned above:
[tex]\begin{gathered} a+b>c \\ b+c>a \\ a+c>b \end{gathered}[/tex]In this case, knowing two sides of the triangle, you can set up that:
[tex]\begin{gathered} a=28\operatorname{cm} \\ b=82\operatorname{cm} \end{gathered}[/tex]Let be "c" the third side of this triangle. You know that:
[tex]\begin{gathered} 28\operatorname{cm}+82\operatorname{cm}>c \\ 110\operatorname{cm}>c \end{gathered}[/tex]Therefore, as you can notice, the third side can be less than 110 centimeters.
Based on the explained before, you can conclude that the third side can be:
[tex]\begin{gathered} c<110\operatorname{cm} \\ \end{gathered}[/tex]And it can be:
[tex]\begin{gathered} c>82\operatorname{cm}-28\operatorname{cm} \\ c>54\operatorname{cm} \end{gathered}[/tex]The answers are:
- The longest the third side can be is:
[tex]109\operatorname{cm}[/tex]- The shortest the third side can be is:
[tex]55\operatorname{cm}[/tex]a certain drug is made from only two ingredients compound a and compound B there are 2 L of a compound a used for every 3 ml of compound be if a chemist wants to make 275 mL of the drug how many milliliters of a compound a are needed
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ANSWER
[tex]110mL[/tex]EXPLANATION
We have that for every 2 mL of Compound A, 3 mL of Compound B is used.
This means that the ratio of Compound A to Compound B is:
[tex]2\colon3[/tex]The Chemist wants to make 275 mL of the drug.
To find out how much of Compound A must be used, we have to divide the ratio for Compound A by the total ratio and multiply by 275 mL.
The total ratio is:
[tex]\begin{gathered} 2+3 \\ \Rightarrow5 \end{gathered}[/tex]Therefore, the amount of Compound A to be used is:
[tex]\begin{gathered} \frac{2}{5}\cdot275 \\ \Rightarrow110mL \end{gathered}[/tex]That is the answer.
-3x-6=9x+6 let's if we on the same page
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Answer:
The solution to the equation is;
[tex]x=-1[/tex]Explanation:
Given the equation;
[tex]-3x-6=9x+6[/tex]firstly, let us subtract 6 from both sides;
[tex]\begin{gathered} -3x-6-6=9x+6-6 \\ -3x-12=9x \end{gathered}[/tex]then we can add 3x to both sides;
[tex]\begin{gathered} -3x+3x-12=9x+3x \\ -12=12x \end{gathered}[/tex]lastly, divide both sides by 12;
[tex]\begin{gathered} \frac{-12}{12}=\frac{12x}{12} \\ -1=x \\ x=-1 \end{gathered}[/tex]Therefore, the solution to the equation is;
[tex]x=-1[/tex]
Here are three angles which angle is greater than 90 degrees
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By definition:
1. A Right angle is an angle that measures 90 degrees.
2. An Obtuse angle is an angle whose measure is greater than 90 degrees.
3. An Acute angle is an angle whose measure is less than 90 degrees.
A Right triangle is formed when a a vertical line
Which of the following rational functions is graphed below?
A. F(x)= -1/x
B. F(x)= 1/x-1
C. F(x)= 1/x+1
D. F(x)= 1+x/x
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Because we have a vertical asymptote at x = -1, we conclude that the correct option is C.. Which of the following rational functions is graphed below? In the graph, we can see that we have a vertical asymptote at x = -1.. …
Between what two consecutive integers does √68 fall?
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The two consecutive integer which the square root of 68 is in between are 8 and 9 , since the square root of 68 is around 8.25
In simple terms, integers means whole and it can't have a fractional or decimal component. So the answer is 8 and 9
Find an equation for the perpendicular bisector of the line segment whose endpoints are (-1,2) and (9,−2).
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The equation for the perpendicular bisector is 2x + 5y = 8
The slope of the perpendicular bisector is reciprocal to the reciprocal of the slope of the segment connecting the two points. The segment's midpoint must be passed through.
Given endpoints are (-1,2) and (9,−2)
Let us consider (-1, 2) = ([tex]x_{1} ,y_{1}[/tex]) & (9,−2) = ([tex]x_{2} , y_{2}[/tex],)
The formula for slope is
m= [tex]\frac{y_{2} - y_{1} }{x_{2}-x_{1} }[/tex]
⇒ [tex]\frac{-2-2}{9-(-1)}[/tex]
⇒ [tex]\frac{-4}{10}[/tex]
= [tex]\frac{-2}{5}[/tex]
The line passing through the midpoint ([tex]x_{3}, y_{3}[/tex]) = [tex](\frac{-1+9}{2} ,\frac{2-2}{2} )[/tex]
⇒ (8/2, 0/2)
∴ [tex](x_{3} ,y_{3} )[/tex] = (4, 0)
The equation for the perpendicular bisector is
[tex]y - y_{3}[/tex] = [tex]m(x- x_{3})[/tex]
⇒ [tex]y - 0 = \frac{-2}{5} (x-4)[/tex]
⇒ 5y = -2x + 8
2x + 5y - 8 =0
Therefore the required equation is 2x + 5y = 8
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The school that Jill goes to is selling tickets to a play. On the first
day of ticket sales the school sold 6 senior citizen tickets and 2 child tickets
for a total of $50. The school took in $131 on the second day by selling 13 senior
citizen tickets and 10 child tickets. What is the price of one senior citizen
ticket and one child ticket?
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In Linear equation, C = $4 for a child ticket .
What is a linear equation example?
Ax+By=C is the usual form for two-variable linear equations.As an illustration, the conventional form of the linear equation 2x+3y=5 When an equation is given in this format, finding both intercepts is rather simple (x and y).A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.6S+ 2C = 50
13S+ 10C = 131
30S + 10C = 250
13S+ 10C = 131
subtract to eliminate one variable
17S = 119
S = 119/17
S = $7 for a senior ticket
2C = 50 - 6S = 50 - 6 * 7
= 50 - 42
2C = $8
C = $4 for a child ticket
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Write an recursive formula for an, the nth term of the sequence 5, -1, -7,....
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The terms of the sequence are 5, -1, -7
Let us find the common difference between each two consecutive terms
-1 - 5 = -6
-7 - (-1) = -7 + 1 = -6
Then the common difference is -6
The first term is 5
The recursive formula is
[tex]a_1=1stterm;a_n=a_{n-1}+d[/tex]Substitute in the formula the value of the 1st term and d the common difference
[tex]a_1=5;a_n=a_{n-1}+(-6)[/tex]Remember (+)(-) = (-)
[tex]a_1=5;a_n=a_{n-1}-6[/tex]This is the recursive formula for the sequence
Look at the sequence in the table. Which recursive formula represents the sequence shown?A) an = an-1 + 4C) an = 2an-1 + 3B) an = 4an-1 + 1D) an = 2an-1 - 1
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Answer:
The recursive formula for the given sequence is;
[tex]a_n=a_{n-1}+4[/tex]Explanation:
Given the sequence;
[tex]1,5,9,13,17[/tex]The sequence above is an Arithmetic Progression AP.
Writing the recursive formula;
[tex]a_n=a_{n-1}+d[/tex]for the sequence, the common difference d is;
[tex]\begin{gathered} d=17-13=4 \\ d=4 \end{gathered}[/tex]The recursive formula will then be;
[tex]a_n=a_{n-1}+4[/tex]I’m supposed to prove this identity but it’s not working for me
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Given
[tex](cot\theta+tan\theta)^2=csc^2\theta+sec^2\theta[/tex]Explanation
From the left hand sie
[tex]\begin{gathered} (cot\theta+tan\theta)^2=cot^2\theta+2cot\theta tan\theta+tan^2\theta \\ Next \\ since\text{ tan}^2\theta=sec^2\theta-1\text{ and }cot^2=csc^2\theta-1 \\ (cot\theta+tan\theta)^2=sec^2\theta-1+2cot\theta tan\theta+csc^2\theta-1 \\ (cot\theta+tan\theta)^2=sec^2\theta-1+2\frac{cos\theta}{sin\theta}\times\frac{sin\theta}{cos\theta}+csc^2\theta-1 \\ (cot\theta+tan\theta)^2=sec^2\theta-1+2+csc\theta-1 \\ (cot\theta+tan\theta)^2=csc^2\theta+sec^2\theta \end{gathered}[/tex]FDT of weightShow the steps in the construction of the FDT
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Okey Im going to explain you how to fill each part of the chart
Tha main part of the FDT is frecuency, for this you are going to take each weight you have, in order
41
42
44
46
etc...
Then you are going to put the frecuency, the frecuency is the number of times each value is in your data list
41 1
42 1
44 4
46 1
etc ....
Now, in this example they are asking you to set some intervals, on range for the class (minimun, maximum). Then some intervals inside this range, so you dont have to put each possible value. Something like this:
41 to 44 6
45 to 48 5
etc...
Each glass of sparkling cranberry juice combines half a cup of cranberry juice and inc cup of sparkling water. Cranberry juice costs $1.50 per cup, and sparkling water costs $.48 per cup. How much will y glasses of sparkling cranberry juice cost in dollars?
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The cost of y glasses of sparkling cranberry juice is $2. 24
What are algebraic expressions?Algebraic expressions are described as expressions that consist of variables, factors, constants, terms and coefficients.
They are also described as expressions made up of mathematical operations, which includes;
AdditionSubtractionParenthesesBracketDivisionMultiplication, etcFrom the information given, we have that;
Cranberry juice costs $1.50 per cupSparkling water costs $1.48 per cupA glass is a combination of half cup of cranberry and one cup of sparking waterCost of y glasses of sparkling cranberry juice = 1/2($1.48) + 1($1.50)
Find the product
y = $0.74 + $1.50
Add the values
y = $2. 24
Hence, the value is $2. 24
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Solve for x. Round to the nearest tenth, if necessary.N64°хx3.7LM
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The triangle is shown below:
Using the Cosine Trigonometric Ratio,
[tex]\cos \theta=\frac{\text{adj}}{\text{hyp}}[/tex]We can substitute the values as follows:
[tex]\cos 64=\frac{3.7}{x}[/tex]Solving, we have
[tex]\begin{gathered} 0.4384=\frac{3.7}{x} \\ \therefore \\ x=\frac{3.7}{0.4384} \\ x=8.4 \end{gathered}[/tex]The value of x is 8.4
the angle of elevation for the first Hill of a roller coaster is 55°. If the length of the track from the beginning to the highest point is 98 ft what is the approximate height of the roller coaster when it reached the top of the first Hill? options, 80 ft, 98 ft, 56 ft, 43 ft
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Using trigonometric property in the figure,
[tex]\sin \theta=\frac{opposite\text{ side}}{hypotenuse}[/tex][tex]\begin{gathered} \sin \text{ }55^{\circ}=\frac{h}{98\text{ }} \\ h=98\times\sin 55^{\circ} \\ \cong80\text{ ft} \end{gathered}[/tex]Here, h is the height of the hill.
Therefore, the approximate height of the of the roller coaster when it reached the top of the first Hill is 80 ft.
Option A is the answer.
pls help me ty i feel this should be easy
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The value of x and y if [tex]T_{(-2,7)}(x,y)=(3,-1)[/tex] are 5 and - 8 respectively.
When a figure is relocated from one place to another without changing its size, shape, or orientation, a transition known as translation takes place.
We have,
[tex]T_{(-2,7)}(x,y)[/tex] = ( 3, - 1 )
The translation of T( - 2, 7 ) acts in the way as:
[tex]T_{(-2,7)}(x,y)[/tex] = ( x - 2, y + 7 )
Now, it is given that:
[tex]T_{(-2,7)}(x,y)[/tex] = ( x - 2, y + 7 ) = ( 3, - 1 )
Comparing the points,
We have,
x - 2 = 3
Adding 2 on each side of the equation,
x - 2 + 2 = 3 + 2
x = 5
And;
y + 7 = - 1
Subtracting 7 from each side of the equation,
y + 7 - 7 = - 1 - 7
y = - 8
Hence, the value of x and y are 5 and - 8 respectively.
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Mandy opened a savings account and deposited 100.00 as principal the account earns 15%interest compounded quarterly how much will she earn after 5 years
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We can solve this by means of the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where A is the amount of money saved after a time t, r is the rate of interest in decimal, n is the number of times interest is compounded per year and P is the initial amount deposited in the account.
From the statement of the question we know:
P = $100
r = 0.15
n = 4
t = 5 years
we can replace these values into the above formula, to get:
[tex]A=100(1+\frac{0.15}{4})^{4\times5}=208.81[/tex]Then, after 5 years she will have saved $208.81, subtracting the initial amount of money deposited we get the money earned, like this:
money earned = $208.81 - $100 = $108.81
Then, Mandy earns $108.81 after 5 years.
help me pleasee!!
thank you
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Answer:
what population census
You deposit $5000 in an account earning 4% interest compounded monthly. How much will you have in the account in 15 years?
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The amount of money in the account in 15 years for a deposit of $5000 at 4% interest rate is $9,101.51.
What is the accrued amount in the account in 15 years?The compound interest formula is used to calculate the growth of money using interest compounding.
Compound interest is expressed as;
A = P( 1 + r/n )^(n×t)
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $5000Interest rate r = 4%Compounded monthly n = 12Time t = 15 yearsAccrued amount A = ?First, convert the rate from percent to decimal.
Interest rate r = 4%
Interest rate r = 4/100
Interest rate r = 0.04
To determine the amount of money in the account in 15 years, plug the given values into the formula above and solve for A.
A = P( 1 + r/n )^(n×t)
A = 5000( 1 + 0.04/12 )^( 12 × 15)
A = 5000( 1 + 0.04/12 )^180
A = $9,101.51
Therefore, the accrued amount in 15 years is $9,101.51.
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Find the value of x and y.
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By applying the Pythagorean theorem and employing tan values, the values of x and y are 9 and 18, respectively.
The Pythagorean Theorem is what?According to the Pythagorean Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
Since base is known to be and tan theta is perpendicular to base,
theta = 30 and x is the perpendicular here.
tan 30 = x/[tex]9\sqrt{3}[/tex]
tan 30 = 1/[tex]\sqrt{3}[/tex]
= x/[tex]9\sqrt{3}[/tex]
x = 9
Using the Pythagorean theorem,
[tex]y^{2} =x^{2} +(9\sqrt{3}) ^{2}[/tex]
the answer is 324: =81+81(3)=81+243
y = [tex]\sqrt{324}[/tex]
y = 18
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find the measure of the missing angle round to the 1 decimal place
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To find the missing angle we can use the inentity for cos tha is:
[tex]\cos (\theta)=\frac{adyacent}{hypotenuse}[/tex]and in our triangle will be:
[tex]\cos (\theta)=\frac{24}{30}[/tex]and we cn solve for theta:
[tex]\begin{gathered} \theta=\cos ^{-1}(0.8) \\ \theta=36.9º \end{gathered}[/tex]graph the equation using the point and the slopey-2=1/5(x-1)
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point-slope form of a line:
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope and (x1, y1) is a point on the line.
In the case of:
[tex]y-2=\frac{1}{5}(x-1)[/tex]the slope is 1/5 and the point is (1, 2)
With this information, we can deduce that the point (1+5, 2+1) = (6, 3) is on the line. Connecting these two points we can graph the line as follows:
Teresa purchased a prepaid phone card for $25. Long distance calls cost 19 cents a minute using this card. Teresa used her card only once to make a long distance call. If the remaining credit on her card is $17.02, how many minutes did her call last?Please help me. Its due in a couple of hours.
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We have that the prepaid phone card has $25 but Teresa used it and then it has $17.02, then the difference is:
[tex]25-17.02=7.98[/tex]this means that Teresa spent $7.98 on her call, then, if one minute costs 19 cents (or $0.19), then, dividing 7.98 by 0.19 we have:
[tex]\frac{7.98}{0.19}=42[/tex]therefore, Teresa called for 42 minutes.
In the circle, what is the measure of ZACB? 60° 20° 80 40°
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The given problem is an example of an "inscribed angle"
The inscribed angle ∠ACB is half of the intercepted arc AB
[tex]\angle ACB=\frac{1}{2}\text{mAB}[/tex]The intercepted arc AB is 40°
So, the inscribed angle ∠ACB becomes
[tex]\begin{gathered} \angle ACB=\frac{1}{2}(40\degree) \\ \angle ACB=20\degree \end{gathered}[/tex]Therefore, the measure of ∠ACB is 20°
How many driveways can you and your friend shovel in 1 hour?
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-[tex]\frac{12}{7}[/tex]-[tex]\frac{11}{8}[/tex]
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LCD( lowest common denominator is 56)
[tex] - \frac{12 \times 8}{7 \times 8} - \frac{11 \times 7}{8 \times 7} \\ = - \frac{96}{56} - \frac{77}{56} \\ = - \frac{ 173}{56} [/tex]
ATTACHED IS THE SOLUTION
Dave opens a savings account that has an annual simple interest rate of 0.1%. If he initially deposits $1500, find the amount in the savings account after 5 years.
Answers
Answer:
$1,507.51502
Step-by-step explanation:
so we know that %0.1 percent is 0.01. so you are gonna multiply 1500 by 1.001 (just adding the intrest) and then you will get 1501.5. the multiply that by 1.001 again and then then thatanswer and repeat 3 more times and then you get $1.507.51502
Solve for h
The height is ____ cm
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[tex]V=\cfrac{Bh}{3} ~~ \begin{cases} V=216\\ B=36 \end{cases}\implies 216=\cfrac{36h}{3} \\\\\\ 216=12h\implies \cfrac{216}{12}=h\implies 18=h[/tex]
Measure the width of a standard sized piece of paper (printer paper works great) in millimeters. Choose the answer that best represents the correct number of significant figures allowed by the ruler and is closest to your measured value.Group of answer choices216 mm215.9 mm21.59 mm
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the width of a standard sized piece of paper in millimeters is 215.9mm
therfore from the grooup of answer choices, the second option which is 215.9mm is the correct answer
which option below is the correct domain and range of the following function? f(x)= x^1/3 *PHOTO*
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The Solution:
Given:
[tex]f(x)=x^{\frac{1}{3}}[/tex]Required:
Find the domain and range of the given function.
Below is the graph of the function:
From the above graph, we have the domain and the range as:
[tex]\begin{gathered} Domain=(-\infty,\infty) \\ \\ Range=(-\infty,\infty) \end{gathered}[/tex]Answer:
[option B]
